DCDS
Hölder stability of diffeomorphisms
Jinpeng An
Discrete & Continuous Dynamical Systems - A 2009, 24(2): 315-329 doi: 10.3934/dcds.2009.24.315
We prove that a $C^2$ diffeomorphism $f$ of a compact manifold $M$ satisfies Axiom A and the strong transversality condition if and only if it is Hölder stable, that is, any $C^1$ diffeomorphism $g$ of $M$ sufficiently $C^1$ close to $f$ is conjugate to $f$ by a homeomorphism which is Hölder on the whole manifold.
keywords: strong transversality condition structural stability Hölder regularity. Axiom A

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